# Double Robust Bayesian Inference on Average Treatment Effects

arXiv: https://arxiv.org/abs/2211.16298 · HTML: https://mlsanity.com/paper/2211.16298/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 69 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers](https://mlsanity.com/paper/1802.08667/) (2018)
- [Augmented Minimax Linear Estimation](https://mlsanity.com/paper/1712.00038/) (2017)
- [Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations](https://mlsanity.com/paper/1909.02210/) (2019)
- [Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness](https://mlsanity.com/paper/1712.04594/) (2017)
- [Debiased Bayesian inference for average treatment effects](https://mlsanity.com/paper/1909.12078/) (2019)
- [A Bayesian view of doubly robust causal inference](https://mlsanity.com/paper/1701.04093/) (2017)
- [Confidence Intervals for Nonparametric Empirical Bayes Analysis](https://mlsanity.com/paper/1902.02774/) (2019)

## Built on by (most cited first, 4 of 4)

- [Bayesian Semi-supervised Inference via a Debiased Modeling Approach](https://mlsanity.com/paper/2509.17385/) (2025)
- [Bayesian Semiparametric Causal Inference: Targeted Doubly Robust Estimation of Treatment Effects](https://mlsanity.com/paper/2511.15904/) (2025)
- [Generalized Bayes for Causal Inference](https://mlsanity.com/paper/2603.03035/) (2026)
- [Calibrated Inference for the Conditional Average Treatment Effect in the Few-Placebo Regime via Gaussian Processes](https://mlsanity.com/paper/2605.27473/) (2026)

## Abstract (arXiv)

We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct the posterior distribution of the resulting ATE. Both adjustments make use of pilot estimators motivated by the semiparametric influence function for ATE estimation. We prove asymptotic equivalence of our Bayesian procedure and efficient frequentist ATE estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, our method provides precise point estimates of the ATE through the posterior mean and credible intervals that closely align with the nominal coverage probability. Furthermore, our approach achieves a shorter interval length in comparison to existing methods. We illustrate our method in an application to the National Supported Work Demonstration following LaLonde [1986] and Dehejia and Wahba [1999].